as a convert to catholicism, i would definitely - definitely - suggest that you not give people rosaries who are grieving.
even if they ‘graciously accept’ it, they will probably, unless you have a strong relationship with them (which i assume you don’t, since you’re asking our opinion), throw it away. and it will cause them, most probably, to reinforce their ideas that we catholics are mary worshippers and idolators. the person might also suspect that you are trying to use this opportunity to convert them to catholicism.
i would, above all, love the person. usually, loving someone means finding the way in which THEY receive love, and giving it to them. it was posted in an earlier post: ‘At least you will have performed an act of charity from your heart, which is all that really matters.’ i would take issue with the way this is stated. it makes it sound like, as long as we give them something in ‘an act of charity’, even if we don’t take the time to learn how they would receive the act, ‘that’s all that matters. we’ve done our part. if they’re offended, that’s their problem.’
in times like the loss of a loved one, or when in pain, it’s often best to steer clear of doctrinal issues, and especially intertraditional dialog. in times like those, it’s best just to be there, and to love. if you want to express your faith, let them know you’re praying for them, perhaps get them a card.
anything in the way of something so obviously catholic as a rosary, i fear, will be taken the wrong way.
as i said, if you KNOW the person well enough that they will KNOW what you mean by it, then you needn’t ask our advice at all. you KNOW how they’ll take it. but if you’re not sure, steer away from anything that divides rather than unites us with our protestant brothers.